From what I understand, there are different opinions on this. Some rabbis hold that during the process of turning bones into gelatin, the bones go through such a transformation, that they lose the status of having been originally from an animal, and therefore start off “neutral” - that is kosher and non-meat.
Other rabbis hold that if a substance gives form to a food (and this is the case also with the renin in cheese that makes it solid) than it can never lose its non-kosher status, and would therefore need to come from a kosher animal. But the meat status is lost in the process, and therefore the gelatin (or renin) is still not meat.
And yet of course there are other rabbinical opinions that require the bones to come from kosher, non-meat sources, and that gelatin comes from fish bones.
There is also a vegetarian gelatin substitute called agar agar (also called agar by those who don’t like to sound like they’re stuttering). It comes from seaweed, actually one of my cookbooks claims it’s just a particular type of seaweed that has been dried. Since it doesn’t involve animals at all, it can be used in kosher foods as well as vegetarian dishes.
Agar is used as a gelling agent in some foods, such as jello-type desserts. But it doesn’t gel quite as well as the real thing, and the kosher jello brands (e.g. KoJel and others) will note this in their directions. And it is nowheres near good enough for marshmallows, where only real gelatin will work.
To my knowledge, there are three kinds of “kosher gelatin” around:
Some does come from kosher fish. I’ve heard this is good enough for medicine capsules, but again not good enough for marshmallows.
Some rabbis do say that any animal bones can be used, and that the process of making it into gelatin removes the “meat” status so that it can be used with milk products. In theory, this opinion is based on various verses in the Torah which speak about not eating the flesh, nerves, and skin of a non-kosher animal, but glarinngly omits any prohibition of the bones. In practice, however, there are reports (rumors) that those who manufacture this type of “kosher gelatin” do not do a good enough job of cleaning the bones, and so many people who eat only kosher food will avoid this type.
Several years ago a new company began manufacturing kosher gelatin made from bones of kosher animals which were kosher slaughtered and kosher prepared. This type has become accepted by most kosher consumers, and is used in jello-type desserts, marshmallows, and gummi candy.
As to whether any of these are acceptable to vegetarians, you’d have to ask a vegetarian.